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H/W3 Binary to Denary Name ___________________________________ Form ________ H/W Year 8 Homework Booklet Theme 1 Data Representation Computers themselves, and “ software yet to be developed, will revolutionize “ the way we learn. - Steve Jobs Founder of Apple Introduction What language does a computer understand? How does a computer represent data, information and images? Soon, you will be able to answer the questions above! In this theme we will explore the different ways in which data is represented by the computer, ranging from numbers to images. We will learn and understand the number bases and conversions between denary and binary. We will also be looking at units of information, binary addition and how we can convert binary data into a black and white image! See the key below to find out what the icons below mean: Self Assessment: You will mark your work at the start of next lesson. ENSURE YOU COMPELTE HOMEWORK AS MARKS WILL BE COLLECTED IN! Edmodo Quiz: The will be a quiz the start of next lesson based on your homework. SO MAKE SURE YOU REVISE! Peer Assessment: Homework marked by your class mate at the start of next lesson. MAKE SURE YOU HAVE YOUR HOMEWORK DONE SO YOU CAN SWAP WITH ANOTHER PUPIL! Stuck? Got a question? Email your teacher. Mr Rifai (Head of Computing) [email protected] Miss Davison [email protected] Miss Pascoe [email protected] 2 Due Date: H/W1 Data & Number Bases Read and digest the information below. You will be quizzed next lesson! Any set of characters gathered and translated for What is Data? some purpose. How computers see the world There are a number of very common needs for a computer, including the need to store and view data. Computers use electrical signals that are on or off, so they have to see everything as a series of binary numbers. This data is represented as a sequence of 1s and 0s (on and off). All data that we want a computer to process needs to be converted into this binary format. What is binary? Binary is a number system that only uses two digits: 1 and 0. All information that is processed by a computer is in the form of a sequence of 1s and 0s. Therefore, all data that we want a computer to process needs to be converted into binary. The binary system is known as a ‘base 2’ system. This is because: • there are only two digits to select from (1 and 0) • when using the binary system, data is converted using the power of two. What is denary? Denary is a number system that uses 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. This is called a 'base-10' number system, because there are ten symbols involved. Here are some examples of denary numbers: 5 8715 249 316 Quiz Score attained: ____ / ____ 3 Due Date: H/W2 Denary to Binary Use the binary conversion tool below to help you with the task. 128 64 32 16 8 4 2 1 Task 1 - Convert the following denary numbers into binary using 4 bits. 1. 8 3. 15 2. 2 4. 13 Task 2 - Convert the following denary numbers into binary using 8 bits. 1. 65 4. 100 2. 98 5. 255 3. 138 6. 164 Challenge – (You may need more than 8 bits!) 7. 256 8. 300 WWW: EBI: Total: ____ /12 4 Due Date: H/W3 Binary to Denary Use the binary conversion tool below to help you with the task. 128 64 32 16 8 4 2 1 Task 1 - Convert the following 4-bit binary numbers into denary. 1. 0011 3. 1010 2. 0001 4. 1111 Task 2 - Convert the following 8-bit binary numbers into denary. 1. 00010011 5. 10011001 2. 00011100 6. 10101010 3. 00110011 7. 11100000 4. 11111111 8. 00001111 WWW: EBI: Total: ____ /12 5 Due Date: H/W4 Binary Addition Addition Rules Use the binary addition rules to add the following 0 + 0 = 0 binary numbers together. 0 + 1 = 1 Show your working out and where you have carried! 1 + 1 = 0 carry 1 1+1+1=1 carry 1 1. 0110 + 0110 1+1+0 = 0 carry 1 1+1+1=1 carry 1 5. 101110 + 011010 2. 11101 + 11001 6. 1110111 + 0100111 3. 11011 + 01101 7. 11001101 + 00111011 Challenge__________________________________________ 9. 11011 + 101101 10. 101111 + 01110111 WWW: EBI: Peer assessed by: 6 Due Date: H/W5 Units of Information Read and digest the information below. You will be quizzed next lesson! Bit 0 or1 A ‘bit’(short for Binary Digit) is the smallest unit of data that can be stored by a computer. Each ‘bit’ is represented as a binary number, either 1 (true) or 0 (false). Nibble 0110 This is not a very commonly used term compared to bit and byte. It is the term given to a group of four bits. Therefore two nibbles make a byte. The reason it is not very common is because most microprocessors use groups of 8 bits and higher i.e. They use one or more bytes to process data. Not many devices make use of a nibble. Byte 01000001 = A A ‘byte’ contains 8 bits, so for example, it could be stored as 11101001. A single keyboard character that you type, such as the letter A or the letter T takes up one byte of storage. Other groupings and examples include: •Kilobyte (KB) = 1000 bytes Example: e.g. a text file •Megabyte (MB) = 1000 kilobytes e.g. a photograph taken on a phone •Gigabyte (GB) = 1000 megabytes e.g. a high definition film •Terabyte (TB) = 1000 gigabytes e.g. a hard drive in a computer 64GB = 64,000MB 64,000MB = 64,000,000KB 64,000,000KB = 64,000,000,000 bytes! Quiz Score attained: ____ / ____ 7 Due Date: H/W6 Representing Images Have a look at the black and white images below. Use the knowledge gained from the lesson to convert the black and white image into binary and then into denary. The images below are 4x4 and have a total of 16 bits. Binary Denary ___________1000 ___________8 ___________0110 ___________6 1 ___________0001 ___________ ___________0110 ___________6 Binary Denary ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ Binary Denary ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ 8 Due Date: The images below are 8x8 and have a total of 64 bits. Work out the binary and denary values. Binary Denary 00111100 60 Create your own image and work out the binary and denary values. Binary Denary Hint: Google 8x8 pixel images WWW: EBI: Peer assessed by: 9 H/W7 Knowledge Organiser What is Binary? The computer language that is used to represent all data and instructions within a computer. It has a Base of 2 –either 1 or 0 (on of off) What is Denary? Denary is the number base we use in Math. It has a Base of 10 (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) Binary Addition Rules: Units of Measurement: 0 + 0 = 0 Bit –1 or 0 (one binary digit) 1 + 0 = 1 Nibble –4 bits 0 + 1 = 1 Byte –8 bits 1 + 1 = 0 (carry the 1) 1,000 bytes –kB 1 + 1 + 1 = 1 (carry the 1) 1,000 kb –MB 1,000 MB –GB 1,000 GB -TB Convert Binary into Denary: 1. Insert the Binary value into the conversion tool (right to left): 128 64 32 16 8 4 2 1 2. Count the values that have been turned on (with a 1 underneath them) 3. Their total equals the Denary equivalent. Converting Denary into Binary: 1.Start from the left, find the first number on the conversion tool that can go into the denary number and take it away. 2.Repeat this until the Denary number equals 0 and fill any remaining parts of the conversion table with 0’s. 3.This is then you Denary number converted to Binary. 10 Due Date: Pixel is short for picture element. • A pixel is a single point within a bitmap image. • Bitmap Image: a map of bits made up of pixels. • Bitmap images can be represented using binary (on or off –black or white) which then can be converted into binary code Practice 14 in binary using 4 bits 122 in binary using 8 bits 11110000 in denary 10101010 in denary 0101 + 1010 0111 + 1110 11 12.
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